Wellbore trajectory models are used for two distinct purposes. The first use is planning the well location, which consists of determining kick-off points, build and drop rates, and straight sections needed to reach a specified target. The second use is to integrate measured inclination and azimuth angles to determine a well's location.
Various trajectory models have been proposed, with varying degrees of smoothness. The simplest model, the tangential model, consists of straight line sections. Thus, the slope of this model is discontinuous at survey points. All conventional methods of wellbore trajectory calculations are based on assumptions and most of them, in each course, are straight lines, polygonal lines, cylinder helixes, or circular arcs. Another common model is the minimum curvature model, which consists of circular arcs. This model has continuous slope, but discontinuous curvature. Analysis of drillstring loads is typically done with drillstring computer models. By far the most common method for drillstring analysis is the “torque-drag” model originally described in the Society of Petroleum Engineers article “Torque and Drag in Directional Wells—Prediction and Measurement” by Johancsik, C. A., Dawson, R. and Friesen, D. B., which was later translated into differential equation form as described in the article “Designing Well Paths to Reduce Drag and Torque” by Sheppard, M. C., Wick, C. and Burgess, T.
Torque-drag modeling refers to the calculation of additional load during tripping in and tripping out operations where torque is due to rotation of the drillstring. Drag is the excess load compared to rotating drillstring weight, which may be either positive when pulling the drillstring or negative while sliding into the well. This drag force is attributed to friction generated by drillstring contact with the wellbore. When rotating, this same friction will reduce the surface torque transmitted to the bit. Being able to estimate the friction forces is useful when planning a well or analysis afterwards. Because of the simplicity and general availability of the torque-drag model, it has been used extensively for planning and in the field. Field experience indicates that this model generally gives good results for many wells, but sometimes performs poorly.
In the standard torque-drag model, the drillstring trajectory is assumed to be the same as the wellbore trajectory, which is a reasonable assumption considering that surveys are taken within the drillstring. Contact with the wellbore is assumed to be continuous. However, given that the most common method for determining the wellbore trajectory is the minimum curvature method, the wellbore shape is less than ideal because the bending moment is not continuous and smooth at survey points. This problem is dealt with by neglecting bending moment but, as a result of this assumption, some of the contact force is also neglected.
Usually, wellbore trajectories are designed with constant-curvature well defined arcs that act as the transition between the tangent sections of a well path. The transition curves are defined as the curve segments connecting the tangent section of the well path to the build or drop sections of the well path. While the transition between the tangent section and build section or the tangent section and the drop section may appear to be smooth, there may be discontinuity causing various stresses in the tubulars. A discontinuity, for example, is apparent when two circular arcs and one tangent section or a circular arc and a tangent section are used for the well path profile. To avoid this problem, continuous build or drop sections are planned. However, even with these designs, there exists a discontinuity in the transition zones.
Therefore, there is a need for a new wellbore trajectory model that is capable of bridging curves (discontinuity) in the transition zones and may be used with other models, such as the standard torque-drag model, in the design of extended and ultra-extended well paths. There is also need for a new wellbore trajectory model that not only is capable of bridging curves in the transition zones, but also reduces tubular stresses/failures and can be used for designing multilateral well paths.